Resource Use Pattern Analysis for Opportunistic Grids Marcelo - - PowerPoint PPT Presentation
Goals UPA Simulation Implementation Experiments Related Conclusion Resource Use Pattern Analysis for Opportunistic Grids Marcelo Finger Germano C. Bezerra Danilo R. Conde Department of Computer Science (IME-USP) University of S ao
Goals UPA Simulation Implementation Experiments Related Conclusion
Marcelo Finger Germano C. Bezerra Danilo R. Conde
Department of Computer Science (IME-USP) University of S˜ ao Paulo Supported by CNPq/Brazil project 550895/2007-8.
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
1 Opportunistic Grids and Scheduling 2 The UPA Method 3 Simulation 4 Implementation 5 Experiments 6 Related Work 7 Conclusion
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
1 Opportunistic Grids and Scheduling 2 The UPA Method 3 Simulation 4 Implementation 5 Experiments 6 Related Work 7 Conclusion
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Applications for Grid Computing
computationally intensive distributed heterogeneous environments
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Applications for Grid Computing
computationally intensive distributed heterogeneous environments
Opportunistic Grid Computing
Idle time of machines
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Applications for Grid Computing
computationally intensive distributed heterogeneous environments
Opportunistic Grid Computing
Idle time of machines High-performance computation
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Applications for Grid Computing
computationally intensive distributed heterogeneous environments
Opportunistic Grid Computing
Idle time of machines High-performance computation Resource-owners have to give permission
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Applications for Grid Computing
computationally intensive distributed heterogeneous environments
Opportunistic Grid Computing
Idle time of machines High-performance computation Resource-owners have to give permission QoS must remain high
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Applications for Grid Computing
computationally intensive distributed heterogeneous environments
Opportunistic Grid Computing
Idle time of machines High-performance computation Resource-owners have to give permission QoS must remain high
InteGrade: opportunistic grid infrastructure
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Desirable: prediction of resource availability Prediction available for grid scheduler The better the prediction, the lower impact on QoS
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Desirable: prediction of resource availability Prediction available for grid scheduler The better the prediction, the lower impact on QoS Proposed Solution: Resource Use Pattern Analysis
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Consists of: Detecting the local use pattern of each resource at each machine in the grid
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Consists of: Detecting the local use pattern of each resource at each machine in the grid Basic Hypothesis: Each resource has a (temporal) “pattern” of use
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
To develop a method
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
To develop a method that automatically performs resource use pattern analysis
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
To develop a method that automatically performs resource use pattern analysis for machines belonging to opportunistic grids
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Discover the prototypical patterns of use (off-line)
Unsupervised machine learning Clustering analysis
Runtime prediction
Comparing prototypical with “current” pattern of use
Development method:
Simulation: parameter setting Implementation: LUPA module for InteGrade grid
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
1 Opportunistic Grids and Scheduling 2 The UPA Method 3 Simulation 4 Implementation 5 Experiments 6 Related Work 7 Conclusion
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
A resource use object: Sampled at every 5 min Span of 48h used for prediction Resources: CPU use, available RAM, disk space, swap space, network and disk I/O
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
A resource use object: Sampled at every 5 min Span of 48h used for prediction Resources: CPU use, available RAM, disk space, swap space, network and disk I/O Objects represent availability (not only use)
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Resource Use Pattern Analysis
Unsupervised machine learning Obtain fixed number of use classes
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Resource Use Pattern Analysis
Unsupervised machine learning Obtain fixed number of use classes
A class represents a frequent use pattern E.g. busy work day, light work day, holiday, etc
Each class represented by a prototypical object
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Resource Use Pattern Analysis
Unsupervised machine learning Obtain fixed number of use classes
A class represents a frequent use pattern E.g. busy work day, light work day, holiday, etc
Each class represented by a prototypical object
Two phases:
training/learning phase: off-line execution/prediction phase: runtime
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Inputs a large amount of objects Collected from regular operation Clustering is applied to training data Reliability depends on amount of data
At least 60 objects, or 2 months of data.
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Inputs a large amount of objects Collected from regular operation Clustering is applied to training data Reliability depends on amount of data
At least 60 objects, or 2 months of data.
Several parameters have to be set
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Number of clusters: 5, 10
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Number of clusters: 5, 10 Data normalisation: no normalisation, variational
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Number of clusters: 5, 10 Data normalisation: no normalisation, variational Computation of prototypical element: centroid, centre
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Number of clusters: 5, 10 Data normalisation: no normalisation, variational Computation of prototypical element: centroid, centre Similarity measurement: Euclidean distance between points.
Between clusters: single linkage, complete linkage, centroid method, Ward’s method
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Number of clusters: 5, 10 Data normalisation: no normalisation, variational Computation of prototypical element: centroid, centre Similarity measurement: Euclidean distance between points.
Between clusters: single linkage, complete linkage, centroid method, Ward’s method
Clustering algorithms: hierarchical, sequential, k-means, etc.
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Number of clusters: 5, 10 Data normalisation: no normalisation, variational Computation of prototypical element: centroid, centre Similarity measurement: Euclidean distance between points.
Between clusters: single linkage, complete linkage, centroid method, Ward’s method
Clustering algorithms: hierarchical, sequential, k-means, etc. Simulation was performed to choose parameters
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Recent Track Prototypical Element
6 12 18 24 30 36 42 48 25 50 75 100
d1 d2 d3
d3 < d2 < d1 Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Recent Track Prototypical Element
6 12 18 24 30 36 42 48 25 50 75 100
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Recent 24h record is compared against 48h use classes The closest class is the current use class. Predicted future in current use class: [now–48h] Request at 6am can predict 18 hours Request at 6pm can predict 6 hours (only)
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Recent 24h record is compared against 48h use classes The closest class is the current use class. Predicted future in current use class: [now–48h] Request at 6am can predict 18 hours Request at 6pm can predict 6 hours (only) Options for longer predictions:
Use less than 24 of current record.
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Recent 24h record is compared against 48h use classes The closest class is the current use class. Predicted future in current use class: [now–48h] Request at 6am can predict 18 hours Request at 6pm can predict 6 hours (only) Options for longer predictions:
Use less than 24 of current record. Predicts < 48h Chain of predictions (not implemented yet)
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
1 Opportunistic Grids and Scheduling 2 The UPA Method 3 Simulation 4 Implementation 5 Experiments 6 Related Work 7 Conclusion
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Data collected for CPU and RAM use, 120 days Linux machines with very different types of users:
1
a general purpose machine with more than 30 users;
2
a single user machine;
3
a general purpose machine with 6 users;
4
a multi-user machine employed for testing heavy computational linguistics programs.
Several parameters compared
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Correct predictions above 75% in all parameter combinations
Experiments
0.7500 0.8000 0.8500 0.9000 0.9500 1.0000
% Correct
Pure Normalised Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Number of clusters: 5, 10 Data normalisation: no normalisation, variational Computation of prototypical element: centroid, centre Similarity measurement: Distance between clusters: points.
single linkage, complete linkage, centroid method, Ward’s method
Clustering algorithms: hierarchical, sequential, k-means, etc.
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Number of clusters: 5, 10 Data normalisation: no normalisation, variational Computation of prototypical element: centroid, centre Similarity measurement: Distance between clusters: points.
single linkage, complete linkage, centroid method, Ward’s method
Clustering algorithms: hierarchical, sequential, k-means, etc.
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Number of clusters: 5, 10 Data normalisation: no normalisation, variational Computation of prototypical element: centroid, centre Similarity measurement: Distance between clusters: points.
single linkage, complete linkage, centroid method, Ward’s method
Clustering algorithms: hierarchical, sequential, k-means, etc. Simulation validated UPA hypotheses on the use of past patterns to predict future behaviours
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
1 Opportunistic Grids and Scheduling 2 The UPA Method 3 Simulation 4 Implementation 5 Experiments 6 Related Work 7 Conclusion
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Explore ways the scheduling of grid applications using the UPA method
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Explore ways the scheduling of grid applications using the UPA method Compare UPA scheduling with other methods
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Explore ways the scheduling of grid applications using the UPA method Compare UPA scheduling with other methods Identify initialisation strategies
because UPA needs a few months of resource use data collection to be reliable
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
UPA data analysed locally, not centrally
Advantages: privacy, no network traffic due to UPA processing
Local resource Use Pattern Analyser (LUPA) module installed in all grid machines LUPA module is part of InteGrade middleware C++, on several Linuxes
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Data Collection: resource use sampling. Pattern Analyser: off-line clustering. Patterns are recomputed once a day. Predictor: runtime predictions. Interface
double[] getPrediction(resource r, int hours);
returns a vector of values representing the r-use prediction for the next hours, in 5-minute intervals. LUPA is not yet integrated with the scheduler.
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
1 Opportunistic Grids and Scheduling 2 The UPA Method 3 Simulation 4 Implementation 5 Experiments 6 Related Work 7 Conclusion
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Compare UPA scheduling with other methods
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Compare UPA scheduling with other methods Scheduling methods for choosing n machines for h hours:
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Compare UPA scheduling with other methods Scheduling methods for choosing n machines for h hours: RR: round robin. No prediction
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Compare UPA scheduling with other methods Scheduling methods for choosing n machines for h hours: RR: round robin. No prediction last4: Predicts to the future average of last 4h.
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Compare UPA scheduling with other methods Scheduling methods for choosing n machines for h hours: RR: round robin. No prediction last4: Predicts to the future average of last 4h. UPA
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Compare UPA scheduling with other methods Scheduling methods for choosing n machines for h hours: RR: round robin. No prediction last4: Predicts to the future average of last 4h. UPA Predicting methods choose n machines with highest prediction
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
15 machines, logs of 41–120 days Sequence of tests for a fixed set of parameters: n, h Instant tests (1 experiment ≈ 527 tests)
Choose a day with m valid machines 24 tests are executed for 3 methods, each for an hour of the day
performances(t) = 1 − n
i=1 use(mi, t, h)
n
s: scheduling algorithm n: number of chosen machines mi: machine chose to run for h hours starting at t use(mi, t, h): average CPU at mi for [t, t + h]
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45
Experiment
20 40 60 80 100
% Better Performance
UPA last4 equiv
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
UPA last4 Performance Similar to last4, but better Similar to UPA, but worse Impact of ↑ m/n ↑ performance no effect Impact of ↑ h no effect no effect Performance of RR consistently below both last4 and UPA
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Use UPA if more than 21 days of data collection is available; else Use last4 if more than 4 hours of data collection is available; else Predict that resource use at request time persists.
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Running time for pattern analysis was always below 1s Running time for prediction calls was always below 3ms
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Running time for pattern analysis was always below 1s Running time for prediction calls was always below 3ms Measurements made on notebook [AMD Turion 64 1.8GHz CPU, 1GB RAM running Kubuntu 7.10 (32 bits) Linux] Running pattern analysis once a day poses negligible overhead
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
1 Opportunistic Grids and Scheduling 2 The UPA Method 3 Simulation 4 Implementation 5 Experiments 6 Related Work 7 Conclusion
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
BOINC: Volunteer computing Correlated Availability in Internet-Distributed Systems (Kondo, Andrzejak & Anderson, 2008) Computes patterns of simultaneous CPU availability via clustering
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
BOINC: Volunteer computing Correlated Availability in Internet-Distributed Systems (Kondo, Andrzejak & Anderson, 2008) Computes patterns of simultaneous CPU availability via clustering Monitors 112,268 hosts Global monitoring and pattern discovery Several interesting clusters of machines discovered, with potential applications. Not originally intended for scheduling
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
[Roy and Livny, 2003]
Condor:
Combination of dedicated and opportunistic scheduling Opportunistic scheduling based on checkpointing Preemptive resume scheduling No prediction
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
[Roy and Livny, 2003]
Condor:
Combination of dedicated and opportunistic scheduling Opportunistic scheduling based on checkpointing Preemptive resume scheduling No prediction No need to predict job duration
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
[Yang, Schopf and Foster, 2003]
One-step-ahead CPU load prediction
Load Tendency Prediction Increase/decrease adaptation processes
Interval Load Prediction
Average over aggregated CPU load time series
Load Variance Prediction
Standard deviation time series Combined with one-step-ahead prediction
Conservative scheduling: combines interval and variance load prediction
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
1 Opportunistic Grids and Scheduling 2 The UPA Method 3 Simulation 4 Implementation 5 Experiments 6 Related Work 7 Conclusion
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Some form of prediction is always preferable to no prediction UPA method compares favourably w.r.t. other methods Small overheads involved Method can be used for practical grid scheduling
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Some form of prediction is always preferable to no prediction UPA method compares favourably w.r.t. other methods Small overheads involved Method can be used for practical grid scheduling
but needs task duration prediction
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
Scheduler using LUPA information Automated learning of task duration prediction Long term predictions Preemptive task migration using UPA Automated “booking” of machine resources for future executions using UPA
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis
Goals UPA Simulation Implementation Experiments Related Conclusion
mfinger@ime.usp.br
Marcelo Finger, Germano C. Bezerra, Danilo R. Conde IME-USP Use Pattern Analysis